Phase-shifting windowed Fourier ridges for determination of phase derivatives

Determination of the phase or phase derivative from interferometric fringe patterns is an important task in optical interferometry. The use of wavelet ridges was recently shown to be an effective method for phase retrieval from a single fringe pattern. One necessary requirement in this method is the need for carrier frequency. In cases when carrier frequency is not available, the novel phase-shifting windowed Fourier ridges method can be used. Phase derivatives with the proper sign can be directly retrieved even in the presence of noise. An application for curvature determination from speckle shearographic fringes demonstrates the effectiveness of the method.     

Generalized three-dimensional windowed Fourier transform for fringe analysis

A 3D windowed Fourier transform is proposed for fringe sequence analysis, which processes the joint spatial and temporal information of the fringe sequence simultaneously. The 2D windowed Fourier transform in the spatial domain and the 1D windowed Fourier transform in the temporal domain are two special cases of the proposed method. The principles of windowed Fourier filtering and windowed Fourier ridges are developed. Experimental verification shows encouraging results despite a longer processing time.     

Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations

Fringe patterns from optical metrology systems need to be demodulated to get the desired parameters. Two-dimensional windowed Fourier transform is chosen for the determination of phase and phase derivatives. Two algorithms, one based on filtering and the other based on similarity measure, are developed. Some applications based on these two algorithms are explored, including strain determination, phase unwrapping, phase-shifter calibration, fault detection, edge detection and fringe segmentation. Various examples are given to demonstrate the ideas. Finally implementations of these algorithms are addressed. Most of the work has appeared in various papers and its originality is not claimed. Instead, this paper gives an overview and more insights of our work on windowed Fourier transform.     

一种用于动态过程测量的实时偏振相移方法

利用一种特殊的相位龙基光栅和偏振相移技术,可同时获得四幅具有不同相移的干涉图,由此可计算出被测物体的全场相位分布,从而实现对支态过程相位的测量。将该方法应用于马赫－曾德尔干涉系统的散斑干涉系统,分别测量了液体的折射率变化和固体的离面位移,给出了实验结果。     

Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching

Phase demodulation from a single fringe pattern is a challenging task but of interest. A quadratic phase matching and frequency-guided regularized phase tracker (QFGRPT) and a quadratic phase matching and frequency-guided sequential demodulation (QFSD) for demodulation of a single fringe pattern are proposed. The algorithms are characterized by their improvements on both robustness and accuracy, which are realized by quadratic phase matching and frequency guided scanning strategy, respectively. Quadratic phase matching improves accuracy compared with the existing regularized phase tracker techniques and the frequency-guided sequential demodulation technique using linear phase matching. Frequency guidance ensures high robustness compared with the recently published path-independent regularized phase-tracking technique. Demodulation results from computer-simulated and experimental fringe patterns using the proposed methods are demonstrated and analyzed.     

Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB environment

In the process of measurements such as optical interferometry and fringe projection, an important stage is fringe pattern analysis. Many advanced fringe analysis algorithms have been proposed including regularized phase tracking (RPT), partial differential equation based methods, wavelet transform, Wigner–Ville distribution, and windowed Fourier transform. However, most of those algorithms are computationally expensive. MATLAB^® is a general algorithm development environment with powerful image processing and other supporting toolboxes. It is also commonly used in photomechanical data analysis. With rapid development of multicore CPU technique, using multicore computer and MATLAB^® is an intuitive and simple way to speed up the algorithms for fringe pattern analysis. The paper introduces two acceleration approaches for fringe pattern processing. The first approach is task parallelism using multicore computer and MATLAB^® parallel computing toolbox. Since some algorithms are embarrassing problems, our first approach makes use of this characteristic to parallelize these algorithms. For this approach, parallelized windowed Fourier filtering (WFF) algorithm serves as an example to show how parallel computing toolbox accelerates the algorithm. Second, data parallelism using multicore computer and MATLAB^® parallel computing toolbox is proposed. A high level parallel wrapping structure is designed, which can be used for speeding up any local processing algorithms. WFF, windowed Fourier ridges (WFR), and median filter are used as examples to illustrate the speedup. At last, the results show that the parallel versions of former sequential algorithm with simple modifications achieve the speedup up to 6.6 times.     

Smoothing filters in phase-shifting interferometry

The images used in phase-shifting interferometry are usually noisy and smoothing filters are frequently used. Filtering can be done on the fringe patterns before phase retrieving or on the phase map after phase retrieving. Filtering fringe patterns—a form of preprocessing, requires the same processing to be done on at least three patterns. Filtering phase map, on the other hand, needs processing of only one pattern. Preprocessing prevents noise from being carried through while post-processing might clip parts of the signal. Thus there is a need to evaluate which one is better. A theoretical analysis was carried out for this basic problem, followed by computer simulations and a real experiment for verification. The comparison was also extended to phase difference measurement which uses similar but slightly different phase retrieval algorithms.     

Virtual target approach-based optimal guidance law with both impact time and terminal angle constraints

Nonlinear Dynamics - To attack a stationary target with both impact time and angle constraints, a novel two-stage guidance strategy is proposed based on the virtual target approach. A moving...